Integers: Comparing and Ordering

EQ How do we compare and order rational numbers?

Rational Numbers

Rational numbers Numbers that can be written as a fraction. Example: 2 = 2 = 2 ÷ 1 = 2 1

Whole Numbers Positive numbers that are not fractions or decimals. 1 2 3 4 5 6

Integers The set of whole numbers and their opposites. Notes! The set of whole numbers and their opposites. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5

Positive Integers Notes! Integers greater than zero. 0 1 2 3 4 5 6

Negative Integers Notes! Integers less than zero. -6 -5 -4 -3 -2 -1 0

Comparing Integers Notes! The further a number is to the right on the number line, the greater it’s value. Ex: -3 ___ -1 < -5 -4 -3 -2 -1 0 1 2 3 4 5 . . -1 is on the right of -3, so it is the greatest.

Comparing Integers The farther a number is to the right on the number line, the greater it’s value. Ex: 2 ___ -5 > -5 -4 -3 -2 -1 0 1 2 3 4 5 . . 2 is on the right of -5, so it is the greatest.

Comparing Integers The farther a number is to the right on the number line, the greater it’s value. Ex: 0 ___ -2 > -5 -4 -3 -2 -1 0 1 2 3 4 5 . . 0 is on the right of -2, so it is the greatest.

Ordering Integers Notes! When ordering integers from least to greatest follow the order on the number line from left to right. Ex: 4, -5, 0, 2 -5 -4 -3 -2 -1 0 1 2 3 4 5 . . . . Least to greatest: -5, 0, 2, 4

Ordering Integers Notes! When ordering integers from greatest to least follow the order on the number line from right to left. Ex: -4, 3, 0, -1 -5 -4 -3 -2 -1 0 1 2 3 4 5 . . . . Greatest to least: 3, 0, -1, -4

Try This: a. -13 ___ 4 b. -4 ___ -7 c. -156 ___ 32 On your notes. < a. -13 ___ 4 b. -4 ___ -7 < c. -156 ___ 32 < d. Order from least to greatest: 15, -9, -3, 5 _______________ -9, -3, 5, 15 e. Order from greatest to least: -16, -7, -8, 2 _______________ 2, -7, -8, -16

EQ How do we find the absolute value of a number?

Absolute Value The distance a number is from zero on the number line. Notes! The distance a number is from zero on the number line. Symbols: |2| = the absolute value of 2 Start at 0, count the jumps to 2. -5 -4 -3 -2 -1 0 1 2 3 4 5 It takes two jumps from 0 to 2. |2| = 2

Absolute Value The distance a number is from zero on the number line. Ex: |-4| = Start at 0, count the jumps to -4. -5 -4 -3 -2 -1 0 1 2 3 4 5 It takes four jumps from 0 to -4. |-4| = 4

Solving Problems with Absolute Value Notes! When there is an operation inside the absolute value symbols; solve the problem first, then take the absolute value of the answer. Ex: |3+4| = |7| = 7 Ex: |3|- 2 = 3-2 = 1 Hint: They are kind of like parentheses – do them first!

Try This: 15 12 13 8 |15| = _____ b. |-12| = _____ c. |-9| + 4 = _____ On your notes. |15| = _____ b. |-12| = _____ c. |-9| + 4 = _____ d. |13 - 5| = _____ 15 12 13 8